SOLUTION: if x+y=-1 and xy=-12, find the value of x^2+y^2

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Question 1077838: if x+y=-1 and xy=-12, find the value of x^2+y^2
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
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x%5E2+%2B+y%5E2 = %28x%5E2+%2B+2xy+%2B+y%5E2%29+-+2xy = %28x%2By%29%5E2+-+2xy = (-1)^2 - 2*(-12) = 1 + 24 = 25.

Solved.

The key is to present x%5E2%2By%5E2 as a combination of (x+y) (and possibly its degrees) and xy.

Then to replace in this expression (x+y) by the given number, as well as to replace xy by the other given number.

This way ALWAYS works, in any case you can meet in your practice.